Paper-specific moisture control in a traveling paper web

ABSTRACT

A network-based system and method for providing desired moisture set point values for individual papers lines based on the physical properties of each liner and the atmospheric conditions associated with a corrugator is disclosed. The desired moisture set point values are based on the hygroexpansivity of each individual paper liner. Once the moisture set point value has been determined, a conditioning apparatus adjusts a moisture value for each liner in order to tune the post-warp characteristics of the final corrugated product.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/882,773, filed Aug. 5, 2019, and U.S. Provisional PatentApplication No. 62/934,736, filed Nov. 13, 2019, the contents of whichare incorporated herein by reference.

TECHNICAL FIELD

The application relates generally to the production of corrugatedcardboard, and more particularly, to moisture and temperature controlduring the production of corrugated cardboard.

BACKGROUND

The production of corrugated paperboard products is well known. Briefly,in its simplest form a conventional corrugated paperboard structure ismade by gluing two flat sheets of web material (called ‘liners’) to theopposing flute crests of an intermediate, fluted (i.e. corrugated) sheetof web material (called ‘medium’). Often this is done by applying linesof glue, which can be an aqueous starch-based adhesive, to the flutecrests of the medium and then joining those glue-applied crests to therespective liner in a continuous process. First, a single-faceconstruction is made by joining the first liner to the flute crests atone side of the medium in a single-facer. Then the resulting single-facecomposite is delivered to a double-backer where the second liner isjoined to the opposing flute crests to yield the completed, three-layercorrugated paperboard structure. Such processes are well known, asdescribed for example in U.S. Pat. No. 8,398,802, the contents of whichare incorporated herein by reference.

As each or any of the aforementioned liners and medium gain or losemoisture, the resulting product can warp. That is, loss of moisture froma paper layer can result in shrinkage of the paper due to contraction ofindividual paper fibers within the layer. Conversely, a gain of moisturecan result in expansion of the paper due to swelling of the individualpaper fibers as they absorb water. One problem in conventionalcorrugating has been warpage of the finished corrugated paperboard. Ifthe aforementioned layers, and especially the liners, gain or lose waterin different amounts from the time they enter the corrugating processuntil the time they emerge as the composite three-layered structure, andeven until well afterward, then the corrugated paperboard will tend towarp. That is, as the opposing liners making up the composite expand (orcontract) at different rates or to different degrees, the compositestructure inherently must bend to accommodate them and remain bondedtogether.

Accordingly, it is desirable to maintain as much as possible themoisture content of at least the opposing liners at or near their targetmoisture content on exiting the corrugating process, so that both duringand after that process those layers will not expand or contract relativeto one another. If done successfully, the result will be a corrugatedpaperboard composite that will not post-warp; i.e. that will not warponce it emerges from the corrugating process. Unfortunately,historically this has been easier said than done.

One reason is that in order to facilitate adhesion, the bonding surfacesof the liners typically are heated to promote penetration andgelatinization of the starch adhesive that bonds them to the medium.Moreover, the industry trend has been to use as little starch adhesiveas possible to save both cost and weight. This means that what littleadhesive is used must penetrate and homogenize as much as possiblewithin the opposing bonding surfaces of the adjacent layers. To ensuremaximum penetration and gelatinization for strong adhesion, the paperstypically are heated to near the boiling point of water (i.e. 100° C.).While this heating improves one critical corrugating parameter(starch-adhesion bonding), it negatively impacts another: layer moisturecontent. That is, heating the layers tends to drive out moisture. Thus,the liners go through the corrugating process drier than when theyentered, having been dewatered compared to their initial, as-suppliedstate. As a result, they may tend to shrink (i.e. contract) prior to oreven during the process steps for producing a corrugated product.Because the liners become over dry (i.e. dried to a moisture contentbelow their natural state under prevailing conditions), they will tendto pick up atmospheric moisture once they emerge from the corrugationprocess. Over the next 12-24 hours, as they re-absorb water that wasdriven from them, two factors typically will produce warpage.

First, each liner typically will not re-expand to its pre-driedcondition once it re-absorbs atmospheric moisture, as a result ofhysteresis. This means that even once rehydrated, the liners will notreturn precisely to their original dimensions. Second, the opposingliners can be dried to different degrees during the corrugating process;e.g. because one is carried longer than the other against dryingelements such as steam drums or hot plates in a double-backer. Moreover,in conventional corrugating processes the corrugated medium often is notdirectly artificially heated at all, whereas both opposing liners are.These factors can combine to produce unpredictable or uncontrolleddifferences in the degree of post-corrugation expansion upon rehydrationof the different layers of the corrugated composite, which will producewarp.

Another difficulty is that the gain or loss of moisture for each type ofpaper is unique. Within each nominal paper basis-weight range, incomingpaper layers vary by a number of factors. These factors include furnish,density, polar angle, caliper, hygroexpansivity, hydroexpansivity,moisture resistance, coatings, tensile strength, porosity, and moisturecontent. Adjusting for these and other factors for a specific supply ofpaper in order to control the moisture content, and thus shrinkage, hasproven difficult. One challenge is that the atmospheric conditions (e.g.temperature and relative humidity) for the location where the supply ofpaper is stored will impact the rate of gain or loss of moisture for thepaper. Another challenge is that the relative hygroexpansive propertiesfor different types of paper vary. As discussed below, this means thateven when two paper liners are adjusted to the same moisture content,there still may be warping of the composite structure as the paperfibers in the respective liners gain or lose moisture at differentrates.

Current methods of adjusting the moisture content of paper layersinclude those based on (i) the relative humidity or (ii) the relativehumidity and board weight of the paper layer. For example, the followingrelation is used to set a target moisture percentage for a paper layerbased on the relative humidity of the environment where the paper isstored:H=(relative humidity/10)+1; where relative humidity is in %; e.g. 70% RHwould yield H=8% target moisture content for the paper layer

Alternatively, example target moisture percentages for single-wall (SW)and double-wall (DW) corrugated boards in an environment wherein therelative humidity is <50%, 50%, or >50% are shown in Table 1:

TABLE 1 Relative humidity % Light SW Heavy SW Light DW Heavy DW <50%7.5% 8.0% 8.5% 9.5%  50% 7.0% 7.5% 8.0% 9.0% >50% 6.5% 7.0% 7.5% 8.5%

Of course, the values in Table 1 are generalizations meant to provideranges of acceptable moisture percentages based on broad ranges ofrelative humidity. A difficulty with the above relation and the data inTable 1 is that each manufacturer must modify the target moisturepercentage based on local conditions, which forces the manufacturer tobroaden the range of acceptable moisture percentages. For this approachto work, each manufacturer must constantly fine-tune the properties ofeach individual paper liner (or medium where desired) in order toreproduce corrugated product that meets desired parameters. Thisfine-tuning requires a large amount of time, expertise, and resources.

The '802 patent incorporated above describes adjusting the moisturecontent in each of the three layers (two liners and one medium) to 6-9wt. % prior to heating and joining them to facilitate starch-adhesivebonding. This moisture adjustment is made using a moisture conditioningapparatus as described in the '802 patent, which applies a uniform,thin-film layer of water to (at least) the bonding surface of therespective liners to adjust their moisture content to be within therange of 6-9 wt. % prior to being fed to either the single-facer or thedouble-backer, where it will be heated and bonded to an adjacent layer.The resulting thin-film layer of water protected against over-drying theliners. It was a sacrificial surface layer of water that ultimatelywould absorb (and would be vaporized by) the heat introduced to preparethe liners for corrugating, thus protecting and preserving the moisturealready bound up in the paper fibers. This solution functions in manycases. But it can be improved based on moisture-absorption properties ofpaper webs and the atmospheric conditions that affect them, which werenot previously appreciated.

For example, even with a sacrificial moisture layer and concurrentadjustment of the moisture content of each web-material layer to 6-9 wt.%, post-warp still can be observed in some corrugated products.

Moreover, in conjunction with the aforementioned moisture adjustment the'802 patent explains it still can be desirable to regulatemoisture-application in the cross-machine direction to compensate forcross-web variations in moisture-content, to ensure as littlecross-machine moisture variation as possible. Indeed, conventionalcorrugators typically include complex systems that detect across-machine moisture profile in the traveling paper web, and thenattempt to normalize that profile by adding moisture at discretecross-machine locations corresponding to low-moisture bands. The goal isto attain an effectively zero-gradient moisture profile in thecross-machine direction. This can minimize or prevent cross-machinewarpage in the finished product resulting from discrete bands ofdifferent moisture content in the web.

The inventor has now discovered an efficient way to compensate formoisture variation in the as-supplied webs without constantly finetuning the operating parameters of the manufacturing process; andwithout corrugator operators having to understand all the factors thatcontribute to post-warp and manually adjust for them. The inventor'ssolutions disclosed herein also dispense with the aforementioned complexsensing and localized moisture-application equipment designed to measureand apply moisture at discrete cross-machine locations of a travelingweb. Not only is such equipment expensive and its operation complex, butit has exhibited limited reproducibility in terms of post-warp outcomes.

SUMMARY

In accordance with one aspect of the present invention, a method ofproducing a corrugated product is provided. The method includesadjusting a moisture content in a first face-sheet web to a first rangeof greater than 10 wt. % and up to 30 wt. % by applying a first thinfilm of liquid to a first surface thereof. The method further includesheating the first face-sheet web and thereafter bonding the firstsurface of the first face-sheet web to a first side of a fluted medium.

In accordance with another aspect of the present invention, a method ofproducing a corrugated product is provided. The method includesmeasuring or assigning a first hygroexpansivity attribute value for afirst face-sheet web, and then determining a first moisture-conditioningsetpoint for the first face-sheet web based on said firsthygroexpansivity attribute value. The method further includesconditioning the first face-sheet web by applying a thin film of aliquid to the first face-sheet web to adjust a moisture content thereinwithin a first range of greater than 10 wt. % and up to 30 wt. %according to the moisture-conditioning setpoint value.

In accordance with another aspect of the present invention, a method ofconditioning a traveling web is provided. The method includes (i)assigning a first hygroexpansivity attribute value to a first liner tobe used in making a corrugated composite; (ii) determining a firstmoisture setpoint value for the first liner based on the firsthygroexpansivity attribute value; and (iii) conditioning the first linerby applying a first thin film of a liquid to the first liner to adjustits moisture content based on the first moisture setpoint value.

In accordance with another aspect of the present invention, a method ofcorrugating is provided, which includes (i) receiving from a pluralityof corrugators a plurality of respective corrugator input data setsrelative to conditions prevalent and/or feedstock materials used at therespective corrugators to produce corrugated products, each saidcorrugator input data set comprising data values pertaining to any orall of: relative humidity, temperature, pressure, and composition andmoisture content of the feedstock materials; (ii) aggregating saidplurality of corrugator input data sets in a data storage, wherein saiddata sets and/or individual data values therein have been correlatedwith hygroexpansivity attribute values representative ofhygroexpansivities of paper webs; (iii) receiving specific corrugatorinput data comprising data relating a first face-sheet web used or to beused at a specific corrugator for making a specific corrugated product;(iv) comparing the specific corrugator input data against the aggregateddata sets in said data storage and identifying or calculating therefroma first hygroexpansivity attribute value representative ofhygroexpansivity behavior of said first face-sheet web; (v) based onsaid first hygroexpansivity attribute value, determining a firstmoisture-conditioning setpoint for said first face-sheet web calculatedto adjust a moisture content therein to be within a first range ofgreater than 10 wt. % and up to 30 wt. %; and (vi) transmitting saidfirst moisture-conditioning setpoint to said specific corrugator for usein making said specific corrugated product

In accordance with another aspect of the present invention, anetwork-based system for producing a corrugated product is provided. Thesystem includes a central site adapted to receive via the Internetcorrugator input data from a plurality of remote corrugator controlterminals each being respectively adapted to collect corrugator inputdata specific to an associated corrugating operation. The central siteincludes data-storage means for storing the corrugator input data and aprocessor for evaluating the corrugator input data and determininghygroexpansivity attribute values therefrom. The processor is furtheradapted to assign moisture-conditioning setpoints for the respectivecorrugating operations based on said hygroexpansivity attribute values.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top-level schematic block diagram illustrating exampleprocess steps and associated equipment for methods of making compositecorrugated board.

FIG. 2 is a schematic diagram of an example moisture conditioningapparatus 100 that can be used in a corrugating method.

FIG. 3 is a schematic diagram of a network-based system that can be usedto obtain and record hygroexpansivity attribute values for paper liners,and to assign predictive values for such attributes to papers based ondata values.

FIG. 4 is a chart depicting preferred glue line widths in inches byflute size.

DETAILED DESCRIPTION

As used herein, when a range such as 5-25 or >5 up to 25 is given, thismeans preferably at least 5 or preferably >5, and separately andindependently, preferably not more than 25.

It has been determined that by tabulating the moisture content and otherfeatures of individual paper liners, the hygroexpansivity of anindividual paper liner can be determined. Then the hygroexpansivitycharacteristics of different papers having different attributes can bestored in a database. Once the hygroexpansivity of a particular paperhas been determined or is known (empirically or predictively), one canestablish a specific moisture setpoint value for the individual paperliner, in combination with such setpoint values as are determined forother paper layers in a composite board, in order to tune the post-warpcharacteristics of that board. To understand this, first a basicunderstanding of how paper webs absorb water, and importantly how theystore, give up, and transfer that water, will be helpful.

A paper web is composed of a network of intermingled and enmeshed fibersthat define the web. Those fibers define interior fiber spaces withinthe cellular structure of the individual fibers themselves. They alsodefine an interstitial space, which is essentially the free or voidspace located outside individual fibers but within the excluded volumeof the overall web defined by the network of fibers. In this manner, apaper web is not unlike a sponge, which is a solid network of fibrousmaterial that defines an intricate system of pores and canals, thelatter constituting the void space within the sponge geometry.

Similar to a sponge, a paper web generally holds and transports water intwo ways. The first of these is superficial, wherein the paper web canabsorb and carry water in the interstitial space defined between andoutside of individual paper fibers, but within the void space of thefiber network. The absorption and retention of water in thatinterstitial space is largely dictated by the mechanics of flow (i.e.water applied to the surface of the web will tend to flow through thatspace in response to hydrodynamic forces, including gravity). Theprincipal impediment to flow through the interstitial space will be thepressure drop associated therewith (though surface-tension forces alsowill produce wicking), which can be overcome via application of externalforces or increased pressure gradient across the paper web. Absorbedwater also can be expelled via application of a mechanical force (e.g.compressing the paper web to shrink its volume and thus drive out theincompressible water from the interstitial space). Under such externalpressure, the liquid water generally will flow out from the interstitialspace rapidly and easily.

The second way in which paper can hold and transport water is intrinsic,wherein individual fibers of the web absorb and elute moisture toachieve a dynamic equilibrium at the prevailing humidity of thesurrounding environment. Absorption and retention of water in thismanner, within the paper fibers, is based on the principles ofequilibrium and will be governed by the laws of thermodynamics. Thus,the principle driving force for absorption within paper fibers is nothydrodynamic pressure (meaning that simply squeezing or pressing waterinto the paper will not efficiently hydrate the fibers). Rather, it isthe moisture concentration gradient across the fiber membrane, betweenthe interior fiber space and the surrounding environment. Here, moisturewill traverse the fiber membrane at a rate proportional to that gradientand to a permeation constant specific to the particular papercomposition and the fiber porosity (i.e. factors that are largely immuneto external influences). Unlike the interstitial space, it generallytakes an extended period for moisture to be introduced within the fibersof the web to equilibrate the fiber with the humidity of theenvironment. The delay in fiber moisture-reabsorption (or -desorption insome cases), particularly to different degrees in the opposing liners,is what causes a corrugated product that emerges flat from thecorrugating process to exhibit post-warp up to 24 hours later.

Even though moisture can take time to enter individual fibers based on athermodynamic process, it can be driven out rapidly through artificialheating when preparing the web to be bonded via a starch adhesive. Suchheating rapidly raises the water temperature in the fibers and convertsit to steam, which expands and permeates outside of the fibers fasterthan liquid water. Notably, the same two factors generally will governpermeation out from the fibers even upon such heating: concentrationgradient and permeation constant. However, in the form of steam boththese factors favor rapid expulsion of water from the fibers. First,moisture flashed to steam within individual paper fibers is likely to beaccompanied by a similar phenomenon for moisture in the interstitialspace from the same heat. But evolved steam in the interstitial spacewill readily travel through the porous network of the web until it isexpelled. This will result in a moisture concentration gradient favoringexpulsion of steam from within the paper fibers to the interstitialspace via diffusion. Second, the permeability coefficient is temperaturedependent and high temperatures will increase the permeability of steamthrough the fiber walls. The result is that heating against a hot platecreates conditions that will facilitate rapid expulsion of moisture frompaper fibers according to the prevailing thermodynamic system.Conversely, in the absence of such heat on exiting the corrugationprocess, a paper web whose fibers have been dewatered in this mannerwill not re-absorb that moisture so rapidly. This means that althoughmoisture can be readily expelled from within paper fibers on heating inthe corrugating process, it will not be so rapidly re-absorbed once thatprocess ends.

Water absorbed in the interstitial space of a paper web contributes tohydroexpansion, i.e. expansion resulting from swelling via separation ofthe fibers (as opposed to swelling of the fibers themselves) as thefiber network expands to accommodate the absorbed moisture in theinterstitial space. Conversely, water absorbed within the paper fibersthemselves contributes to hygroexpansion; i.e. expansion resulting fromswelling of the individual fibers as they expand to accommodate boundwater. Hygroexpansivity refers to the potential for a given paper (orpaper fibers) to expand or contract based on the absorption or expulsionof water within or from the paper fibers. It is an intrinsic materialproperty of a particular paper that depends on: (i) individual fibercharacteristics, and (ii) the fiber density in the finished paper liner.These characteristics are impacted by prevailing conditions when thepaper is made, and by the composition of that paper. These include theprevailing relative humidity, temperature, pressure, and chemicalcomposition of the fibers.

In addition, as discussed more fully below it has been shown that themagnitude of hygroexpansivity for a given paper system decreasessignificantly with successive humidification cycles from its as-made,i.e. original hygroexpansivity, at least initially. By ‘humidificationcycle,’ it is meant the absorption and subsequent expulsion of waterinto/from the fibers making up the particular paper layer. This meansthat by subjecting a paper layer to successive layers of hygroexpansiveabsorption and desorption, one can effectively reduce the magnitude offuture expansions and contractions based on subsequent hygroexpansiveabsorption/desorption cycles. Though uncertain, the inventor believesthis observed phenomenon may be due to hysteretic effects. Specifically,the inventor has observed that reduction in effective hygroexpansivityfor a given paper layer can be achieved by increasing the moisturecontent of a paper layer to greater than 10 wt. % and then heating it(e.g. via steam drums or hot plates) prior to adhering to adjacentlayers. The observed reduction is similar to that achievable throughsuccessive humidification cycles via (presumed) hysteresis. Withoutwishing to be bound by theory, perhaps when water is first applied to apaper layer via a thin-film, metered moisture application, the fibershave sufficient time to absorb that moisture and expand via bothhydroexpansion and hygroexpansion. Whereas, when the thus wetted paperlayer is subsequently heated by wrapping over a steam drum prior toadhering to adjacent layers, the supplied thermal energy may drive outat least some of the fiber-absorbed moisture effectively carrying out afirst humidification cycle. Alternatively, due to the excess of moisturesupplied, it is possible that within the paper a series ofhumidification cycles are carried out locally over the steam drum (i.e.vaporization and driving of moisture from fibers, followed bycondensation and reabsorption, followed again by vaporization anddriving out) to achieve a number of rapid humidification cycles. It hasbeen discovered that the degree of reduction in hygroexpansivity for agiven paper can be controlled up to a maximum degree of reductioncompared to the as-supplied hygroexpansivity of the paper. For a givenpaper layer, the maximum degree of hygroexpansivity reduction isbelieved to be substantially fixed by properties of the paper itself.Moreover, different (e.g. opposed) liners may have differenthygroexpansivity-reduction maxima. But by fine-tuning the amount ofmoisture added via the thin-film metering system and the amount of heatintroduced, e.g. via steam drums prior to adhering adjacent layers, onecan tune the degree of such reduction up to and including that maximumfor each liner—for example to match that of an opposing liner, ifdesired.

Compared to hydroexpansion (from water in the interstices of the paperweb), the magnitude of hygroexpansion (based on absorption within paperfibers) is roughly 2 to 3 times greater for a given volume of waterabsorbed, at least prior to reducing the hygroexpansive potentialthrough humidification cycling. Stated another way, a given volume ofwater absorbed within the fibers of a paper web will tend to result inexpansion roughly 2-3 times greater than if that same volume of waterwere absorbed only in the interstitial space of the web. Practically,this means that if a protective coating of moisture applied prior toheating a paper web is insufficient to uniformly isolate the fiber-boundmoisture against being vaporized and driven away, then the resultingcorrugated product may be deceptively flat due to over drying within thepaper fibers themselves. Their delayed re-expansion then will tend tocause post-warp. That is, if all moisture from within the fibers isdriven away during the corrugating process, then due to the slow(equilibrium-based) reuptake of moisture into the fibers, any moistureadjustment during the corrugating process will have been entirely withinthe interstitial space. Confined to only the interstitial space of theweb a moisture adjustment within 6-9 wt. % at first will appear to haveyielded flat board within an idealized moisture-content range. However,once the fibers re-absorb moisture to restore equilibrium up to 24-48hours later, the web is likely to deflect 2-3 times more than ifresorption were limited to the interstitial space. More simply,significant post-warp still may occur despite that the operator made theintended 6-9 wt. % total-moisture adjustment during the corrugatingprocess as described in the '802 patent.

Complicating things further is the fact that the degree ofhygroexpansion changes (i.e. is reduced) following humidification cyclesas noted above, presumably due to hysteresis. This also is discussedfurther below. But if the number of humidification cycles is unknown oruncontrolled, especially between opposing liners that may or may not beof the same material, this variable (presumed) hysteretic effect canyield unpredictable and uncontrolled comparative hygroexpansion of theopposing liners, which contributes to unpredictable warpage.

Not only can fiber-reabsorption result in unexpected post-warp, but evenif it is anticipated, adjusting to compensate can prove difficultbecause the precise end dimensions of the web will depend on not justone, but a number of variables, which can be difficult to predict ormodel accurately. These include:

-   -   a) the degree of intra-fiber moisture reabsorption that will        occur, which can vary across the web because different areas may        have been better protected based on minor localized variability        in the conventional protective 6-9 wt. % moisture layer applied        prior to heating, which narrow range represents an idealized        condition;    -   b) consequent (and presumably hysteretic)        variable-hygroexpansivity effects, which will introduce further        variability particularly to the hygroexpansivity of the        individual paper layers; and    -   c) atmospheric conditions that are unique to the local        environment of the manufacturer.        Notably, over-drying a paper web during corrugating (e.g. to        facilitate bonding) in a manner that drives moisture from its        fibers can yield 1% or greater shrinkage in the cross-machine        direction because of hysteresis. This shrinkage cannot be        corrected by remoistening or rehydration during the time period        available during manufacture. Any recovery of moisture within        the paper fibers will occur downstream of the corrugator after        the papers are bonded together and may create dimensional        instability. While this shrinkage will occur uniformly, it is        most noticeable in the cross-machine direction, which is finite        for a given web. Additionally, seasonal changes alter the        atmospheric conditions at each paper supplier's and corrugator's        facilities. For example, the atmospheric conditions (e.g.        temperature, relative humidity, etc.) at a corrugation site in        July will be different than the conditions at the same site in        February. These conditions impact the degree of drying for each        paper layer, and thus can impact the amount of warpage exhibited        in the final corrugated product.

As will be appreciated by now, hygroexpansion (resulting in moistureabsorption in or elution from paper fibers) is the most impactful factorcontributing to post-warp. Not only does it result in a materiallygreater degree of expansion or shrinkage compared to water transportinto/from the paper via other mechanisms, but it also can be the leastpredictable between different liners in the same corrugated composite.Therefore, if the hygroexpansivities of the paper layers introduced to acorrugating machine to form the liners of a given corrugated productwere known, then one could introduce precisely the correct amount ofexcess moisture individually to each such layer to ensure that eachabsorbs an appropriate amount to both protect its fibers from beingoverdried (yielding significant shrinkage), and condition those fibers(via presumed intra-corrugating hysteretic cycles) to tune/reduce therespective hygroexpansivities in order to prevent post-warp. To do thiseffectively, one must also know the incoming water content of each suchlayer, the prevailing conditions at the corrugation site, and theprevailing conditions downstream in which the finished corrugatedproduct is to be stored or used. With this information, and providedthat the corrugation system includes a mechanism to apply ahigh-resolution, precisely metered water layer, the applied moisturecould be tuned to account for all these factors so that both the degreeand rate of expansion/contraction are matched between the liners of acorrugated composite. If the expansion rates and degrees for bothopposing (or all) liners are matched, then there will be minimal or nowarpage as they expand/contract together.

In practice this may be easier said than done because, as noted above,hygroexpansivity has a significant and sometimes unpredictable effect onthe expansion properties from liner to liner, or even for the same linerat different moments in time depending on the conditions it hasundergone. As will be appreciated, cross-tuning highly volatilevariables between opposing liners so that they will match can bedifficult, even if they could be measured empirically. However, as alsonoted above, data has shown that the magnitude of hygroexpansivity for agiven paper layer tends to decrease significantly through successivehumidification cycles, presumably due to hysteresis. Accordingly, inaddition to knowing the hygroexpansivities of opposing liners for acorrugated composite, it also is desirable to reduce their magnitudes,for example via hysteretic humidification cycling, prior to adhering theliners to adjacent layers (e.g. medium) in the corrugator. By bothreducing the hygroexpansivities of the opposing liners, and tuning theirrespective moisture content prior to adhering them to the medium, onecan not only match the expansive behavior between the liners, but reducetheir magnitudes. The former helps reduce or eliminate post-warp, whilethe latter ensures that imperfect moisture-tuning between the linerswill have the least possible contribution to generating post-warp,because any post-warp deflections due to mismatched shrinkage will besmall.

In addition to or in conjunction with reducing hygroexpansivity asdescribed above, it also is preferable to apply a sufficientlyprotective, sacrificial layer of liquid water in substantial excess ofwhat has been conventionally contemplated, to the bonding surface ofeach liner. This excess moisture layer can at least partially isolatebound moisture within paper fibers to prevent them from being overdriedthrough heating during the corrugation process. This can help suppresspost-warp of a corrugated structure by reliably preserving thefiber-bound moisture in the paper webs, and particularly the liners.

Balancing the moisture-layer application to, on the one hand yield asacrificial layer (to protect the fibers from being over-dried), whileon the other hand tune for an appropriate amount of moisture to adjust(reduce) the hygroexpansivity to a desired degree, can be an iterativeprocess. In addition to these effects, one also should consider howapplied moisture will affect the internal stresses of the paper web.As-supplied, paper webs generally include formed-in internal stressesbased on conditions and the resulting fiber configuration as-formed.These stresses result in internal mechanical forces being exerted withinthe paper web, which can be inhomogeneous and contribute additionaldimensional instability that further promotes post-warp. Applying aprecise, excess sacrificial moisture layer also can help reduce theseinternal stresses if sufficient moisture is applied so that themoistened paper can be dried under restraint, and thus stress-relievethe web.

Specifically, it is known that when a paper web is dried under restraintinternal stresses within the paper web can be reduced or eliminated. Byapplying the substantial excess moisture as disclosed herein suchstresses can be reduced, and the overall tensile strength of the liners(and thus of the finished corrugated product) can be increased throughstress relief of the paper fibers in those webs. As already discussed,paper swells when wetted and then contracts as it dries, whichinherently introduces some stress relief to the paper fibers. Moreover,when a thoroughly wetted paper web is dried under restraint (i.e. undertension), the contractile force of shrinking paper fibers acts againstthe tensile force that draws the paper in the machine direction, whichintroduces a substantial amount of stress relief in the web. Forexample, depending on its basis weight the wetted paper web is subjectedto drying under tension forces ranging from 8 kg/meter to 180 kg/meter.This phenomenon, known as ‘drying under restraint’ in the literature,typically has been studied in paper making and not in drawing paper websthrough a corrugating process. However, the inventor believes the sameprinciples would apply here. Accordingly, a substantially wetted paperweb (such as webs 18, 19) that dries under tension in the corrugatingprocess, aided by heat delivered (e.g. from preheaters upstream of wherethe webs are adhered to the medium), will exhibit internal contractileforces that draw against the overall web tension and yield stressrelief, and increased tensile strength in the machine direction. Usingthis process, machine-direction tensile-strength increases in the rangeof 2.5-10% compared to the incoming webs 18, 19 is to be expected.Notably, such increase in tensile strength due to drying under restraintis not observed at the conventional, relatively low-moisture content towhich existing processes adjust the webs (e.g. 6-9 wt. % before thepreheaters in a corrugating process). This phenomenon is only to beobserved when adjusting that moisture content within the range disclosedherein; i.e. >10 wt. % up to 30 wt. %, and preferably 11-15 wt. %.

Although applying a sacrificial water layer to paper webs forcorrugating is known, the water is applied in such low amounts thatdried-in stress is never relieved. And as noted above conventionalprocesses tend to over dry the liners. Together, these factors combineto retain internal stresses within each liner, which contribute todimensional instability in the liner that compounds post-warp resultingfrom hygroexpansion of the liner. In other words, it is desirable toreduce both hygroexpansivity and internal stress in each liner. Both canbe achieved using a material excess of moisture applied in a sacrificiallayer to the bonding surface of each liner, as described below.

It has been found that increasing the moisture content in the liners toa level above conventionally-accepted levels (e.g. greater than 10 wt.%; preferably greater than 10 wt. % and up to 30 wt. % as describedbelow), via application of a uniform, metered thin-film of moistureapplied to the bonding surface, helps to improve the dimensionalstability of the liner, and thus the corrugated product. The disclosedsystems and process apply such a layer, which is effective to: isolateand protect fiber-bound moisture (preventing overdrying and resultinghygroexpansive post-warp), reduce the magnitude of hygroexpansivebehavior (via presumptive hysteretic cycles within the fibers themselveswhile being heated), and stress-relieve the paper web by drying it underrestraint (i.e. under tension) over hotplates or heated drums to themore conventional 6-9 wt. % on emerging from the corrugating process.

In other words, by raising the moisture content in the liners and thendrying under restraint, the magnitude of hygroexpansivity in the linersis reduced while protecting fiber-bound moisture, and internal stressesin the paper are relieved, all of which contribute to more dimensionallystable corrugated product. Most of the drying of the liner occurs priorto combining the liner with the medium, such as when the liner is on aheated surface under tension. For example, the liner is dried undertension when it passes over the heated surface of a preheater, asingle-facer pressure roll, or a single-facer belt. However, the bondingsurface of the liner remains moist in order to accept starch into theliner.

As the dimensional stability of each liner is improved with thedisclosed systems and process, the properties of the final corrugatedproduct are also improved. Conventional systems result in asynchronoushygroexpansion of liners that results in irreversible creep strain,which leads to failure in the corrugated product. By reducing thehygroexpansion of the liners, the properties of the corrugated productwill be enhanced, resulting in a more stable and long-lasting corrugatedproduct.

An example corrugator setup will now be briefly described. A blockdiagram of an example corrugating apparatus 1000 is shown schematicallyin FIG. 1. In the illustrated embodiment, the corrugating apparatusincludes a moisture conditioning apparatus 100 (FIG. 2), a web heatingarrangement 200, a single-facer 300, a glue machine 400, and adouble-backer 500. These components are arranged in the recited orderrelative to the machine direction of a web of medium material 10 as ittravels along a machine path through the corrugating apparatus 1000 toproduce a finished corrugated product 40 exiting the double-backer 500.As will become apparent, the medium material 10 will become thecorrugated web to which the opposing first and second face-sheet webs 18and 19 will be adhered to produce the finished corrugated board 40. Thecorrugator setup described and illustrated here with respect to FIG. 1is substantially the same as that described in detail in U.S. Pat. No.8,398,802 incorporated by reference above. The same setup having similarand alternative features and as described in the '802 patent can beutilized in the methods disclosed herein. Specifically, the samemoisture conditioning apparatus 100 (including a thin-film meteringdevice 130) described in the '802 patent (where it is used to conditionpaper webs to 6-9 wt. % total moisture) can be used to apply thesubstantial excess of moisture to the bonding surfaces of the medium andliners (and web if desired) as described herein. The moistureconditioning apparatus 100 can be operated and adjusted in the mannerdescribed in the '802 patent, to apply an appropriate metered thin-filmof water to achieve the desired >10 wt. % up to 30 wt. % of moisture ina paper web as called for herein, to achieve the herein disclosedsurprising combination of effects, which yield much-improved dimensionalstability.

The first face-sheet web 18 in FIG. 1 will supply the first liner forthe finished corrugated product 40 on exiting the corrugator. Prior toapplying the first face-sheet web 18 to the corrugated medium material10 as in the conventional process (e.g. disclosed in the '802 patent),it is conditioned to adjust its moisture content to achieve the combinedeffects described above of: protecting fiber-bound water to prevent overdrying, reducing magnitude of hygroexpansivity, and stress-relieving theface-sheet web 18; all of which can be achieved via drying underrestraint (i.e. under tension) against hot plates or heated rollers oncethe required excess-moisture layer has been applied.

The moisture adjustment can be achieved by applying a substantiallycontinuous thin film of water to the first face-sheet 18 to adjust itsoverall moisture content to yield a substantial excess of moisturewithin the desired range as herein disclosed. The water layer can beapplied to the side of the web 18 that will be down to (i.e., directlycontact) a heat source prior to contacting flutes of the web of mediummaterial 10, on which glue has been applied, for bonding thereto in thesingle-facer 300.

The resulting single-faced web 20 (composed of the web of mediummaterial 10 adhered to the first-face sheet 18, preferably both of whichby now have been moisture conditioned) exits the single-facer 300 andenters the glue machine 400 where glue is applied to the remainingexposed flute crests in order that the second face-sheet web 19 can beapplied and adhered thereto in the double-backer 500.

The single-faced web 20, having glue applied to the exposed flutecrests, enters the double-backer 500 where the second face-sheet web 19is applied and adhered to the exposed flute crests and the resultingdouble-faced corrugated assembly is pressed together.

Prior to entering the double-backer 500, the second face-sheet web 19,which will supply the second liner to the finished corrugated product40, is conditioned similarly as the first face-sheet web 18 describedabove to apply a metered thin film of moisture to achieve a substantialexcess moisture content within the range disclosed herein. Preferablythis layer of moisture is applied to the bonding surface of the secondface-sheet web 19, which will be bonded to the exposed flute crests ofthe web of medium material 10 via glue.

It is contemplated that application of excess moisture in the form of athin-film, metered layer of water to the bonding surface of at least thewebs that will form the liners of the composite corrugated product (i.e.first and second face-sheet webs 18 and 19) will yield enhancedpost-warp suppression by several mechanisms as described in detailabove. That is, the sacrificial excess moisture layer will at leastpartially isolate fiber-bound moisture from pre-heating of the linerwebs (i.e. the face-sheet webs 18 and 19) to prepare them for bonding,thus preserving much of their intrinsic moisture content throughout thecorrugation process. It also will supply excess moisture that can beeffective to reduce hygroexpansivity in the liners by supplyingsufficient water to undergo a plurality of (believed) humidificationcycles. And finally, the excess of moisture will be sufficient that asthe face-sheet webs 18 and 19 are dried under tension, e.g. againstheated rollers or hotplates as described in the '802 patent, those webswill be stress-relieved through being dried under restraint.

According to preferred embodiments the moisture content of theaforementioned webs will be so adjusted as to be greater than 10 wt. %;preferably greater than 10 wt. % and up to 30 wt. %; more preferablygreater than 10 wt. % and up to 20 wt. %; and most preferably 11 wt. %to 15 wt. % or 12 wt. % to 15 wt. % or 12 wt. % to 14 wt. %, e.g.utilizing Moisture-Conditioning Parameters supplied by a Central Site620 as will be hereafter described. It is most important that the liners(e.g. face-sheet webs 18 and 19) that will be adhered to opposing sidesof a corrugated medium layer are conditioned as disclosed herein. Unlikethe liners, the web of medium material is corrugated, and the resultingcorrugations can function as accumulators of deflection. Accordingly,post-corrugation deflections in the corrugated medium will be lesspronounced, because they can be taken up to a large degree by the sinuscorrugations therein. Moreover, the opposing liners also act toconstrain the medium from opposite directions, also minimizing theimpact of post-warp in the medium layer. However, if desired the mediumcan be conditioned similarly as described here for the liners.

To apply the desired thin films of water to the respective webs 18 and19, preferably a moisture application roller 120 is used as part of aliner conditioning apparatus 100. Notably, this liner conditioningapparatus 100 is substantially the same as the moisture conditioningapparatus 100 illustrated in FIG. 2 and described in the '802 patent forapplying the corresponding layer of moisture, albeit to achieve a lowermoisture content. On entering the liner conditioning apparatus 100, theliner 18, 19 can optionally be fed first through a pretensioningmechanism 110 and then past a moisture application roller 120 wheremoisture is added to the liner 18, 19 to adjust its moisture content inthe desired range prior to exiting the medium conditioning apparatus100. Still, in other examples, the liner 18, 19 can be fed directly pastthe moisture application roller 120. Moisture is applied to thecircumferential surface of the moisture application roller 120 using afirst thin film metering device 130. This device 130 is illustratedschematically in FIG. 2 in the moisture conditioning apparatus 100 andis useful to coat a very precisely metered thin film or layer of liquidonto the surface of the roller 120 from a reservoir. To achieve themoisture content desired here, preferably the application roller 120 ismetered so that it carries a liquid-water film thickness on its surfaceof greater than 5μ and up to 100μ, and more preferably greater than 10μand up to 50μ. Ideally, the moisture application roller 120 of theapparatus 100 is operated at a surface lineal velocity less than 90%that of the web (18 or 19) conveyed thereagainst, including any speed inthe opposite direction of travel of such web. It also is preferred thatthe dwell distance of the paper web against that roller 120 (i.e. thelineal path length over which a segment of that web is in contact withthe moisture application roller 120) is more than 15 mm and up to 100mm, preferably more than 50 mm and less than 80 mm, for line speeds of450 meters per minute or lower. These dwell-distance ranges can beadjusted proportionately for line speeds above 450 meters per minuteaccording to the following relation:(New Range)/(Range Given Above)=(Final Line Speed in mpm)/(450 mpm)

Mechanisms and roller configurations to adjust the wrap angle, andtherefore dwell distance, of a traveling web against the moistureapplication roller 120 are known in the art (e.g. as described in the'802 patent). Dwell distance is preferred over dwell time as a measureof application-roller contact because given the diameter of conventionalapplication rollers and the line speeds of conventional corrugationprocesses (e.g. 450 m/min as noted above), dwell times will not bematerially or perhaps even measurably different for ranges of contactbetween the traveling web and the moisture application roller 120 thatcan have a material impact on the total amount of moisture applied.Whereas, dwell distances based on the circumferential area of contactover the application roller 120 will be far more readily observed,measured and controlled, and are easily correlated to applied moisturecontent in weight percent to a given traveling web in a givencorrugating process.

Applying a substantial excess of moisture to a traveling web prior toheating it to facilitate bonding (e.g. >10 wt. % up to 30 wt. % moistureto either of face-sheet webs 18 or 19), as a thin-film metered layerapplied to the bonding surface of that web, can provide significantadvantages as noted above. First, by applying such a layer of moistureto the bonding surface before pre-heating, the substantial thin film ofsurface moisture acts as a sacrificial moisture layer that vaporizesnear instantly on contacting pre-heating rollers or hot plates, suchthat the resultant vaporized steam rises up through the paper web, whereit nearly immediately re-condenses to vapor (water droplets) anddelivers its heat of fusion to the web. In this manner, thermal energyapplied initially at only the outer (bonding) surface of the web, isapplied to and absorbed by the paper web itself more diffusely, and moreevenly, thereby reducing the temperature gradient through the thicknessof the web. This vaporization-and-recondensation mechanism also mayyield a humidification cycle that effectively contributes to reducingthe hygroexpansivity of each liner as described above. Also, because thevast majority of that thermal energy must be absorbed by thesurface-present sacrificial moisture layer to supply its heat ofvaporization before additional heat is available to penetrate and affectfiber-bound moisture, the fiber-bound moisture is largely protected frombeing completely vaporized and driven from the fibers. Moreover, theaforementioned substantial excess of moisture renders it less likelythat thermal energy will break-through to vaporize and drive outfiber-bound moisture, thus preserving that moisture.

Although some excess interstitial moisture introduced by the sacrificiallayer may dry after the finished corrugated product has been produced,as noted above the resulting hydroexpansion (contraction) will be afraction in magnitude compared to the hygroexpansion as would resultwere all the fiber-bound moisture driven off and then re-absorbed. Theresulting smaller-magnitude contractions based on loss of interstitialmoisture, and based on both reduced and matched hygroexpansivities ofthe opposing liners, are more likely to be both: a) uniform in theopposing liners (webs 18 and 19) if they are coated similarly withexcess sacrificial moisture layers—meaning that the net post-warp wouldbe zero because the opposing liners will balance one another out; and b)small enough as not to result in unacceptable post-warp.

Yet another benefit of adjusting the moisture content in the preferredexcess range disclosed herein is that it can result in automaticallyleveling the cross-machine moisture content of a web withoutweb-profiling sensors, equipment or feedback control. In addition to thebenefits described above, applying excess moisture to the webs 18 and 19in a preferred range, e.g. >10 wt. % and up to 30 wt. %, via amoisture-application roller 120 having a water-film thickness of >5μ upto 100μ, yields an excess of applied moisture that will facilitateenhanced penetration of liquid and vaporized moisture through the porestructure of the web by wicking and associated interstitial absorption.Such wicking will tend to be greater in cross-machine bands of the webthat are dryer, and it will tend to be least in such bands that arealready well wetted or saturated. The result is that the paper will tendto inherently self-balance its cross-machine moisture content until itsfull cross-machine interstitial expanse is uniformly wetted via absorbedmoisture, which will inherently reduce and perhaps eliminate any othercross-machine warping effects. The excess moisture application in theranges described here supplies sufficient total moisture to allow thisto reliably occur.

Thus, a proper balance of excess-applied moisture will present thecooperative effects of safeguarding the intrinsic moisture of the paperweb (i.e. fiber-bound moisture) and stress-relieving the paper asalready described, minimizing and cross-tuning the hygroexpansivity ofthe opposing liners of a corrugated composite (even further reducingpost-warp), and minimizing cross-web localized moisture gradients thatmay have been introduced in manufacturing or otherwise by the moistureapplication roller 120 itself. Conversely, too much excess moisture(e.g. above the aforementioned parameters of not more than 100μwater-film layer on the application roller 120, or more than 30 wt. %moisture present in the web 18, 19 after moisture application) canresult in entrainment of the web pore structure adjacent to the bondingsurface where the moisture layer was applied. This can inhibitpenetration and uniform wicking as described above, which maydeleteriously affect both cross-machine auto self-leveling of the paperweb as well as fiber-bound moisture preservation.

Cross-machine direction auto-leveling of paper webs using themethodologies described here can be particularly important inlinear-corrugating operations. Unlike conventional corrugating, inlinear corrugating the corrugated medium possesses flutes that runparallel to the machine direction, such that they are glued to theopposing liner webs (18, 19) along glue lines running parallel to andalong the length of those webs. Because of the way paper webs typicallyare manufactured, the potential for shrinkage (due to loss of moisture)is three times greater in the cross-machine direction than in themachine direction. This is due to the orientation of the fibers beingprimarily in the machine direction, as well as the fact that it iseasier to maintain the web under restraint (i.e. under tension) in themachine direction while drying (e.g. by increasing tension differencesbetween successive dryer sections through incremental speed ratiochanges).

Accordingly, variable moisture bands in the cross-machine direction of atraveling paper web (e.g. one or both of web(s) 18, 19) can beparticularly problematic in terms of cross-machine direction warpage(shrinkage). For example, if there are bands that are overdried, or thatshrink at different rates or to different magnitudes, relative to otherbands—or to the opposing liner 18 or 19 opposite the web of mediummaterial 10—then unpredictable and uncontrollable cross-machine warpagecan occur.

In conventional corrugated products, where the flutes extend in thecross-machine direction, those flutes contribute cross-machine stiffnessthat largely resists or counteracts shrinkage as may otherwise occur dueto a variable cross-machine moisture profile. However, in linearcorrugating the flutes extend along the machine direction, and along thelength of the finished corrugated product. These machine-directionflutes contribute their stiffness along the length of the corrugatedproduct, and present little resistance to cross-machine shrinkage. As aresult, a linear corrugated product will have a much greater potentialfor cross-machine shrinkage compared to a conventional corrugatedproduct made under identical conditions.

The presently disclosed auto-leveling technique, when applied at leastto the webs of liner material 18 and 19, minimizes or effectivelyeliminates cross-machine shrinkage by ensuring that the paper is bothuniformly wetted and uniformly protected against uncontrolled intrinsic(bound) moisture-loss in the cross-machine direction. Thus, even if webshaving variable cross-machine moisture bands are fed to a linearcorrugating apparatus, e.g. that disclosed in U.S. Pat. No. 8,771,579(incorporated herein by reference in its entirety) as the opposingliners, by conditioning them as herein disclosed little to nocross-machine warpage or shrinkage can be achieved.

Importantly, the aforementioned cross-machine direction auto-levelingaffect is inherent to the operation of the system as described, ifsufficient moisture is applied to allow for it and so long as too muchexcess moisture is not (i.e. >10 wt. % up to 30 wt. % depending on theapplication). That means that a corrugation system operated as describedhere can exclude web-profiling apparatus designed to measure and thenadjust the cross-machine direction moisture content in the web. In otherwords, it is not necessary to incorporate moisture-detection sensors atdiscrete cross-machine locations of the traveling web to providefeedback control. It is equally not necessary to discretely applymoisture to relatively low-moisture bands in the web. When operated asdescribed here, a moisture conditioning apparatus 100 can be used tosupply sufficient excess water to adjust the moisture content in thetraveling paper web to be within the range of >10 wt. % to 30 wt. %(more preferably 11 wt. % to 15 wt. %), which will yield a robustsacrificial moisture layer on the bonding surface of each of the liners(webs 18, 19) to achieve hygroexpansivity-mediated post-warp control.

The selective absorption of excess deposited moisture in dryer moisturebands to achieve auto-leveling is largely automatic due to fasterwicking and absorption rates of dryer paper. But web tension also playsa role and is subject to limited adjustment in order to enhance theeffect. Specifically, the greater the web tension against amoisture-application roller 120 as it traverses that roller, the greaterthe moisture transfer into the paper web. In a given web, cross-machineweb bands that are relatively dry will have shorter paper fibers thanthe mean fiber length in the paper. This is because dryer fiberstypically contracted or at least are un-swollen relative to wetterfibers. Conversely, relatively wetter web bands will have longer paperfibers compared to the mean fiber length in the web for the oppositereason. As will be appreciated, shorter fiber lengths generally willresult in relatively higher localized tension in dryer web bands,whereas longer fiber lengths generally will result in relatively lowerlocalized tension in wetter web bands. The overall result is that for agiven web traversing a moisture application roller 120 at a given meanweb tension (e.g. depending on basis weight, tension of from 8 kg/meterto 180 kg/meter), dryer bands will tend to have a nominally highertension (e.g. tension of 12 kg/meter to 270 kg/meter) than the mean,such that they are tensioned slightly more strongly against theapplication roller 120. Whereas wetter bands will tend to have anominally lower tension (e.g. tension of 5.3 to 120 kg/meter) such thatthey are tensioned slightly less strongly against the roller 120. Thisvariable-tension effect will tend to cause moisture from the water filmon the application roller 120 to be driven more strongly intolower-moisture bands than into higher-moisture bands, thus enhancing theauto-leveling effect when applying a substantial excess of moisture tothe web.

To enhance this effect, the roll-speed ratio between the applicationroller 120 of the moisture conditioning apparatus 100 and the travelingweb 18, 19 can be adjusted to regulate, and enhance, web tension againstthe roller 120. As used herein, this roll-speed ratio is defined as theratio of the surface lineal speed of the application roller's 120circumferential surface, to the linear speed of the web 18, 19 tensionedagainst and traveling over (a portion of) that surface. Thus aroll-speed ratio of 100% would mean that the surface lineal speed of theroller's circumferential surface is traveling in the same direction andat the same speed as the web 18, 19 thereagainst—meaning effectivelyzero slippage therebetween. For most conventional paper basis-weights(typically 45-500 GSM), in conjunction with the preferred water-filmthickness and dwell distance ranges herein disclosed, it is desirable tooperate the application roller 120 at a roll-speed ratio at least 5%deviant from 100% (either overspeed or underspeed), and more preferablyat least 10% deviant from 100% (either overspeed or underspeed), but inthe same direction as the web 18, 19 is traveling. As will beappreciated, the latter means roll-speed ratios greater than 110% orless than 90% depending on whether the roller 120 is operated atoverspeed or underspeed, respectively. Ideally, the roll-speed ratio isadjusted consistent with these ranges in order to increase the localizedweb tension at the application roller 120 by 15-30% of the baseline webtension in the corrugating process; the latter of which typically ismaintained at from 10 to 25 percent of the web's ultimate tensilestrength. For example, when the baseline web tension in the corrugatingprocess is 8 kg/meter to 180 kg/meter, the localized web tension at theapplication roller 120 may be 9.2 kg/meter to 234 kg/meter. Importantly,the roll-speed ratio also is a data point that can be included in thecorrugator input data and cross-classified against hygroexpansivityattribute values described below, and used to predictively model suchvalues.

From the standpoint of moisture-application and penetration to achieveauto-leveling, over- versus under-speed operation is not believedcritical. Thus, this selection may be based on extrinsic factors relatedto the upstream or downstream operation of the overall corrugationsystem, recognizing that overspeed operation will increase upstream webtension and underspeed operation will increase downstream web tension.Reverse-direction operation of the application roller 120 (i.e.resulting in negative roll-speed ratios) generally is not desired exceptfor medium to heavy basis-weight paper webs, e.g. 125-325 grams persquare meter (GSM) or greater. In any event, it is contemplated thatreverse-direction operation should be avoided for web basis weightsbelow 70 GSM.

Importantly, it is believed that the enhanced dimensional stability andself-leveling effects described here will be achieved via application ofthe noted excess-moisture to only one surface of each of the liner webs(i.e. webs 18, 19) with the bonding surface typically preferred. Butsatisfactory results can be achieved by applying a single layer to thenon-bonding surface if machine layout considerations require it. Thougha moisture layer can be applied to both sides of each of liner webs 18and 19, it is believed that application of the moisture as describedhere to only the bonding (or the opposing) surface will achieve thedescribed dual benefits of both machine-direction and cross-machinepost-warp reduction, such that dual-side application will be unnecessaryand therefore is less preferred.

It was particularly unintuitive that one can effectively compensate forvariable moisture bands in a web by applying a uniform thin film ofwater to the web. Contrary to conventional methods of localizedmeasuring and metering of web-moisture content cross-machine, theinventor applies a constant-thickness, uniform excess water film to theliner webs 18, 19, with no localized measuring or metering, and relieson natural processes to normalize the cross-machine moisture content inthe web. It was surprising and unexpected that cross-machine localizedmoisture gradients could be nulled out via application not of localizedand tuned amounts of moisture as is conventional, but of aconstant-thickness excess-moisture layer across the full width of theweb. The fact that this process can be executed without closed-loopfeedback control to tune precise moisture-application at discretelateral locations across the web width is a substantial advantage overconventional systems because it will save the significant capital andoperating cost required to incorporate localized, cross-machinemoisture-applicators and the associated sensor-based feedback controlloops. In sum, the fact that this process can be executed automaticallyso that it is inherently and reliably auto-self leveling incross-machine direction moisture, and in the absence of any sensors orother feedback control, was a surprising result.

Moreover, methods disclosed herein run contrary to conventional wisdomand industry norms for applying moisture to face-sheet webs 18 and 19for producing liners in corrugated products. As disclosed in the '802patent, it is conventional to adjust the moisture content in those websto be within the range of 6-9 wt. % moisture, prior to preheating thosewebs to facilitate starch bonding to the web of medium material.Applying additional moisture was considered unnecessary to protect thepaper from dehydration through heating. Indeed, applying additionalmoisture would have been undesirable because such excess would wasteboth water and energy, and add cost. It is for this reason that in the'802 patent the moisture-conditioning adjustment of the webs isprecisely controlled to be within the range of 6-9 wt. %. But theinventor has discovered that applying additional excess moisture canyield the aforementioned cross-machine direction auto-leveling effect,essentially turning bad liner-web source stock (that otherwise might nothave been suitable for use in the corrugating process) into acceptablyflat source stock suitable for making corrugated product. At the sametime it can be used to adjust and tune opposing hygroexpansivities ofthe liners making up a corrugated composite to minimize the effects ofpost-warp, and to introduce stress-relief into the paper, in a way notpreviously understood or anticipated. Indeed, as much as 1.5 to 4 timesas much moisture as would have been conventionally applied can be usedto level the paper web and minimize or eliminate the presence ofvariable-moisture bands therein, which will materially reduce or eveneliminate the tendency of the final product to exhibit cross-machinewarpage as known in the art, as well as to minimize shrinkage-basedpost-warp from hygroexpansive and stress effects.

In addition to the improved dimensional stability and auto-self levelingfeatures described above, application of the disclosed excess moistureto the face-sheet webs 18, 19 before preheating also can enable reducingthe amount of starch used to bond those webs to the intermediate web ofmedium material. For example, by adjusting the moisture content in theface-sheet webs 18, 19 (liners) to the range of 6-9 wt. % as disclosedin the '802 patent, when using a typical C-fluted medium and up to 35 #paper stock for all three webs (two liners 18, 19 and one medium), onegenerally achieves penetration depths into the opposing liner webs of1.7 mils as observed in the finished corrugated product, based on astarch-adhesive application rate of 3.5 to 6 g/m² (dry basis, exceptingincidental moisture as is standard). This application rate refers to thetotal starch applied as adhesive to yield the finished corrugatedproduct, and accounts for adhesive application to flutes at both sidesof the medium. However, applying the substantial excess of moisturedisclosed here, one can achieve 25-35% deeper starch penetration fromthe bonding surface of each web 18, 19 under the same conditions, e.g.from about 2.1 to up to about 2.3 mils. This substantial improvement instarch-depth penetration is believed due to lower overall viscosity ofthe adhesive composition once applied to the web 18, 19 (and thusincreased flow through the pore structure of the web), as well asimproved sub-surface starch gelatinization (i.e. expansion). Both ofthese effects in-turn are believed due to the substantial excess ofmoisture available starting from the bonding surface where thestarch-based adhesive composition is applied. That is, the materialincrease in free interstitial water within the sub-surface paper matrixboth promotes deeper penetration of starch granules through increased(lower-viscosity) flow, and facilitates greater gelatinization of starchgranules, which can increase up to two orders of magnitude in volumeupon absorbing available moisture.

Alternatively, using the disclosed process one can achieve comparablepenetration depths as in conventional processes (e.g. ˜1.7 mils) butwith 30% less starch on a solid basis. For example, again for C-flute,to achieve ˜1.7-mil penetration in both the opposing liner webs in afinished corrugated product one need apply only 2.1-4 g/m² starch (drybasis, excepting incidental moisture as is standard) measured similarlyas above.

A similar ˜30% reduction in starch-application rate can achieve similar˜1.7-mil starch penetration for other flute sizes compared toconventional starch-application rates. Table 3 below illustrates typicalnumbers of flutes per foot for a variety of conventional flute sizes,and provides proportions of flute-per-foot compared to C-flute. It isnoted that these values are not standards, as different-sized flutes canbe utilized at different pitches in the corrugated medium. But Table 3is illustrative to demonstrate approximate glue-application rates fortypical pitches of various conventional flutes. According to thedisclosed typical pitches, C flute has around 38 flutes per foot, whileE flute has around 90.

TABLE 3 Flute Typical # Ratio compared Size Flutes/Foot to C-flute A 360.942 B 49 1.283 C 38.2 1.000 E 90 2.356 F 128 3.351 G 179 4.685

The ratio of 90/38.2 is 2.356, meaning that at first glance there shouldbe ˜2.4× more glue for E flute as for C flute according to Table 3.Indeed, as the flutes get smaller one can see the number of glue lines,and presumably the total glue application rate, will increase. But asFIG. 4 shows, the glue line widths also get smaller as the flutes getcloser together. Additionally, the glue line thicknesses get smaller asflute heights get smaller. These two additional factors tend tocounteract the amount of excess glue that may be expected just fromincreasing the number of glue lines (as seen in Table 3), thus reducingthe real difference in glue consumption compared to the ratio of thenumber of flutes relative to C-flute. For example, given the flutespacings and glue-line widths in Table 3 and FIG. 4, theglue-application rate for E-flute is roughly 1.21 times that of C-flute.Other typical comparison percentages are given for other flute sizescompared to C-flute in FIG. 4.

By applying the substantial excess moisture to the liner webs 18, 19 asdisclosed herein, one can reduce the corresponding glue-applicationrates by ˜30% for other flute sizes and yet still achieveindustry-desired starch penetration (solids basis) of roughly 1.7 milsfrom the bonding surface. Note there may be some variability in actualpractice because to achieve the same 30% reduction as with C-flute forother-sized flutes, the paper basis weight for webs of the other flutesizes must be the same. This is rarely the case, and usingdifferent-weight papers for non-C flute webs will impact theproportionate reduction in starch required to achieve comparablepenetration depth in the associated web. However, the basic principalremains that using the disclosed process, a marked reduction in thestarch-application rate (solid basis) to the flute crests for making acorrugated product can result in little to no loss in penetration depthin a given instance. It is contemplated that for typical paper basisweights used for different flute sizes, A through G, when applying thesubstantial excess of moisture as disclosed herein to the liner webs 18,19, starch-application rate reductions of ˜25-35% can result in standard˜1.7-mil starch penetration (solid basis) compared to the applicationrate that otherwise would have been required under identical conditionsusing conventional processes.

Having now recognized the aforementioned relationships, it is desirableto utilize those relationships predictively to predetermine theappropriate amount of moisture to apply to the webs for supplying linersfor corrugated products in a given instance. For example, knowing thestarting moisture content of a particular liner web, and understandingits starting hygroexpansivity behavior and how that behavior is likelyto change based on humidification cycles, as well as understanding thestress-relieving characteristics of drying excessively-moisturized paperunder restraint, one can better determine the appropriate amount ofmoisture to apply to that web to achieve an appropriate pre-heatedmoisture content in the desired range to achieve the disclosed benefits.By tabulating these and other factors for different starting paperstocks and cross-referencing with the conditions prevalent at differentcorrugation installations, one can construct a database to predictivelydetermine appropriate moisture-conditioning setpoints for applying thedisclosed metered liquid layer to achieve appropriate overall moisturecontent for the desired post-warp behavior—and even to tune it (to zero,if desired).

One begins with hygroexpansivity. The hygroexpansivity of each paper maybe calculated, for example, via an empirical relation. The followingempirical relation defines an arbitrary hygroexpansivity value, β, as anormalized difference between the length of a fixed segment of paperobserved at two different values of relative humidity afterequilibration with the humid environment. In this case, β is defined asthe difference in length from equilibration at 85% RH (l₈₅) to 33% RH(l₃₃), relative to a standardized length for that segment (l₀)multiplied by 100.

$\beta = {\frac{\left( {l_{85} - l_{33}} \right)}{l_{0}}*100}$

Of course, as noted above the value for β can be expected to shrinkfollowing successive humidification cycles. This is because the lengthvalues l₈₅ and l₃₃ may be reduced following such cycles, resulting indifferent, smaller values for β. The value of β also is likely to be atleast loosely temperature dependent. So in practical terms, a quantifiedvalue for hygroexpansivity such as β (quantified from the foregoingrelation) may be best used to catalog and characterize the knownhygroexpansive behavior determined through empirical measurement ofdifferent papers made under known, controlled conditions, and to relatethem to predicted hygroexpansive behavior of other papers that are notempirically measured but which are nonetheless made under similarconditions, or which have undergone similar environmental episodes.Quantified values of β from the above relation are less likely to beuseful to denote the absolute hygroexpansivity of a specific paper, fromwhich moisture-adjustment can be tuned.

If one can measure or otherwise assign a hygroexpansivity value orcoefficient to different papers used to make different liners,normalized relative to a substantially common scale or set of parametersfor equating hygroexpansive behavior to manufacturing, experiential andenvironmental conditions, then one will have the basis to predict thehygroexpansive behavior of a given liner, and to tune the pre-adhesionmoisture application to achieve predicted expansive behavior. Mostimportantly, by knowing such values/coefficients for two opposing linersused in the same corrugated composite, one can have a starting point fortuning them relative to one another to effectively and reproduciblyminimize post-warp, or to sustain a desired (tuned-in) degree of warpage(concavity) coming off the corrugator. This is true even though theopposing liners may not be of the same material, the same caliper, fromthe same supplier, etc. —i.e. knowing commonly-grounded hygroexpansivitycoefficients for two opposing liners, one can tune them individuallytoward a final corrugated composite wherein their expansive behaviorwill essentially match. To be clear, the precise empirical relation forcalculating a hygroexpansivity value/coefficient is not critical. Solong as such a value can be calculated or derived for each via a commonmethodology or relation across a range of papers, they all can berelated to identify the relative hygroexpansive behavior characteristicfrom one paper layer to the next, which will enable the sort ofliner-to-liner tuning described here for a given corrugated composite.

Once a database of hygroexpansive characteristics has been establishedfor different papers, environmental factors, etc., another factor thatcan be associated with each paper category is the degree to which itshygroexpansive magnitude can be reduced based on defined environmentalfactors or processing steps. As noted above, it is desirable to reducethe hygroexpansivity of individual paper layers as much as possible, todecrease the magnitude of post-corrugation expansion/contraction, whichwill tend to minimize the magnitude of any post-warp. However, it alsomust be realized that the opposing liners for a given corrugatedcomposite may have different potentials for reducedhygroexpansivity—just like they may have different initialhygroexpansivities based on their respective makeup and other factors.Accordingly, usually it will be desirable to identify a lowest commonhygroexpansivity to which both liners for a given corrugated compositecan be reduced via processing steps, so that their hygroexpansivitiescan be matched at that lowest common value.

An example process contemplated herein includes the following steps: (a)measure or assign a hygroexpansivity attribute value to a liner web thatis to be used in making a corrugated composite; (b) moisture conditionthe liner web to introduce a precisely metered amount of water thereto,taking account of the moisture present in the liner as-supplied to thecorrugating process and the anticipated post-corrugation environmentalconditions; and (c) optionally heat-treating the liner followingmoisture conditioning but prior to adhering to adjacent layers (such asa corrugated medium) to fine-tune the moisture adjustment and to adjustits hygroexpansivity in order to achieve a desired degree ofpost-corrugation hygroexpansion (which can be zero) to minimizepost-warp, or to sustain a pre-determined degree of post-warp. Forreasons already given, the total pre-heated moisture content in theliner web should be within the range of >10 wt. % up to 30 wt. %. Theaforementioned heat-treatment can be utilized to effectively reduce thehygroexpansivity of the liner, comparable to that as may be observed bysubjecting the liner to successive humidification cycles. Indeed, thedegree of hygroexpansivity reduction for a given paper liner under givenconditions (including the degree of heating—based on both heating fluxto the paper and residence time of heating) can be correlated to thatpaper as part of its hygroexpansivity value or characteristic measuredor assigned in step (a) above. This process can be carried out on bothopposing liners for a corrugated composite made via the corrugationmachine, in order that the degree of post-corrugation hygroexpansion ineach is tuned based on or to match that of the other. In this manner,not only can the hygroexpansivity of each liner be tuned to achieve adesired degree of post-corrugation expansion (including substantiallynone, if desired), but the hygroexpansivities of opposing liners can bereduced to a least common degree between them as described above.

If the hygroexpansive properties of respective liners for a desiredcorrugated composite are known, then the least common hygroexpansivityattainable by each of them also can be known. In view of this, and ofthe prevailing atmospheric conditions at the corrugation site anddownstream where the final product is to be stored and/or used, amoisture setpoint value can be recommended and applied as a preciselymetered thin film of water to each paper liner web. The result is thatas the paper layers gain or lose moisture post-corrugation (depending onconditions), the hygroexpansivity of each paper layer is fine-tuned sothat each layer will gain/lose moisture to substantially the same degreeand at substantially the same rate such that any dimensional changesbetween the layers will be matched, minimizing (if not eliminating)post-corrugation warp.

As noted, step (a) above can be carried out by empirically measuring, orcalculating, hygroexpansivity values. It will be possible to calculatesuch values for a given liner in a given application by measuring itspost-corrugation shape-change behavior, knowing its initial moisture aswell as the moisture added prior to the corrugating stages, as well asthe amount of heat energy supplied during corrugating. But evenmeasuring these values directly, for reasons that will be clear abovethey will be useful primarily for papers that are to be corrugated inthe same location and under the same conditions where measured. Theywill be less useful to relate the values for papers measured atdifferent locations under different prevailing conditions, or to valuesmeasured for different papers entirely. Rather, when relating onehygroexpansivity value for one paper to another such value for anotherpaper, those values will be most useful as guidelines to identifystarting points or trajectories for hygroexpansivity conditioningbetween the compared papers. Accordingly, the inventor herein alsocontemplates assigning hygroexpansivity attribute values to paper linersreflective of their hygroexpansivity behavior based on the observedexpansive behaviors of other papers that are known to have been made andused under comparable conditions. By establishing a central database ofhygroexpansive attribute values for different paper liners, andcross-classifying those attributes to other known or measured factorsfor the respective liners, one can assign predictive, data-basedhygroexpansivity attribute values to individual papers based oncomparable papers whose behavior has been observed and the correspondingdata already saved to the database.

In this manner, data-driven, predictive hygroexpansivity attributevalues that reflect true hygroexpansivity can be utilized and assignedto the liners used at different corrugation sites, including liners fromdifferent sources and even mis-matched liners for making thesame-corrugating composite. Those values can be used to establish orrecommend moisture-conditioning settings to introduce proper amounts ofmoisture and heat in order to achieve predictable, controllable degreeof post-warp—for individual liners, or for opposing liners cooperatingwith one another. Such other known or measured factors that can becross-classified or correlated to the hygroexpansivity attribute valuefor a given paper include, but are not limited to: the atmosphericconditions under which they were made, the date and location made andthe machinery or supplier used, the time and conditions of transit tothe corrugator, the prevailing conditions at the corrugator and thecorrugating machinery used, the degree to which particularmoisture-conditioning treatment—including moisture-application andheating—affects or reduces hygroexpansivity, the post-corrugationenvironmental factors, or any other factor that can be measured andtabulated in a database.

FIG. 3 illustrates an exemplary network-based system to obtain, recordand classify hygroexpansivity attribute values for different paperliners. The system can assign predictive values for such attributes topapers being used in disparate corrugation processes based oncross-classified data values known for the papers being used. Thehygroexpansivity attribute values can be measured or calculatedhygroexpansivity values for individual papers as discussed above. Forexample, commercially available apparatus, such as those in theDimensional Stability System (DSS) from Emtec (Leipzig, Germany), may beused to measure the hygroexpansivity attribute values by cycling a webthrough one or more modules in order to wet and dry the web undertension. The DSS may include a first module (e.g. Wet Stretch DynamicsAnalyzer (WSD 02) from Emtec) that is first used to wet a web of paperwith a water-based liquid under adjustable tension and determine thedynamics of the wetted web's expansion. The first module is able tomeasure the paper moistness, humidity, and ambient temperature, and isable to measure the wet expansion range of the web up to a maximum of25% over an unlimited duration. The wetted web may then be dried with asecond module (e.g. Heat Shrinkage Analyzer (HAS) from Emtec), which canmeasure the dimensional stability of the web under a thermal load up to230° C. The second module can measure stretching and shrinkage of theweb by up to 27% and 5%, respectively. A third module (PenetrationDynamic Analyzer (PDA) from Emtec) may be used to measure the rate anddepth at which water is absorbed by the web. By cycling a web throughthe modules (i.e. wetting and drying cycles), the system is able tomimic the changes in both hydroexpansivity and hygroexpansivity thatoccur on a corrugator. The values measured with the first and secondmodules then can form baseline or initial hygroexpansivity attributevalues for a given paper material under the measured conditions.Further, since the modules operate at high frequency (e.g. in themillisecond range), the measured values of each module may be correlatedand modeled to determine the effect of changing different variables inthe system. For example, the system allows a user to see how adjustingthe degree of water penetration in the web impacts the wet stretch ofthe web prior to and during drying. Based on the hygroexpansivityattribute values measured, predictions can be made on the startingmoisture value targets for the top and bottom liners as they exit thecorrugator. In order to refine these target values, and empiricallyderive the hygroexpansivity of the papers, the hygroexpansivityattribute values are compared to the exiting moistures of the top andbottom liner papers (as measured by moisture gauges) that result in flatpaper coming out of the corrugator. This flatness can be as observed andrecorded by the operator or it can be quantified by an online shapemeasurement device, such as a laser.

Alternatively or in addition, and as will be further evident below,hygroexpansivity attribute values can be empirically determined andassigned for a particular paper used in a particular situation based onother known or reported attributes of that paper, as well as of themachinery on which it will be used, its location and the prevalentconditions, all of which can be cross-referenced to prior-observed andrecorded hygroexpansivity behaviors in prior iterations executed on thesame or different corrugating equipment under some or all of the sameconditions. For example, by comparing the moisture differential betweenthe top and bottom liner (or any other paper combination), it ispossible to back calculate the hygroexpansivity of each paper type madeby each paper machine. By collecting such moisture differential values,it is possible to determine when paper suppliers modify their furnishfor different grades of paper, and then adjust moisture parameters basedon those values.

All of these data are aggregated and can be subjected to statisticalcorrelations and analysis, such as an empirical correlation to determinean empirical hygroexpansivity attribute value in a given instance basedon inputs specific to that instance. The inputs can be supplied as partof the Corrugator Input Data, discussed below, for the particularinstance. Alternatively or in addition, hygroexpansivity attributevalues can be tabulated and cross-referenced compared to such inputsbased on the known and previously recorded behaviors for papers undersimilar conditions and having similar attributes previously aggregatedand stored in a database. The hygroexpansivity attribute value will berepresentative of the true hygroexpansivity for the particular paperused the particular situation. It can be an arbitrary quantity devisedvia an empirical correlation or tabular cross-referencing as notedabove, or a combination thereof, so long as it is representative of truehygroexpansivity and consistently determined with other hygroexpansivityattribute values of other papers in other situations (under theirrespective conditions) using the system. Once a hygroexpansivityattribute value is determined for a particular paper, it can be used todetermine an appropriate moisture-application setpoint for thatparticular paper under its prevalent conditions (including the knownstarting and desired endpoints for moisture content), which will besupplied by the user as part of the Corrugator Input Data, discussedbelow.

Returning to FIG. 3, a Central Site 620 includes a Data Storage (such asa server) that is linked via a network 610 to individual CorrugatorControl Terminals 600 that are operatively connected to respectivecorrugators, which can be at the same or at different geographic sites;and which may be operated by different operators or companies. Thenetwork 610 can be a wired or wireless network. It is contemplated thatthe network 610 will operate over the Internet via secure communicationslinks between the Central Site 620 and each Corrugator Control Terminal600.

In order to determine recommended moisture setpoints for each liner (andmedium, if desired) at a given corrugator site, information regardingeach paper layer and the atmospheric conditions from the corrugator siteare assessed. For example, characteristic origin data about each roll ofpaper to be used typically is provided from the paper supplier, often inthe form of a “roll tag.” The origin data includes the paper grade,moisture content on leaving the point of manufacture, caliper,production date, reel position in the paper machine, reel width, reelweight, and paper web length, among other features. The origin dataprovides characteristics about the paper from when the roll shipped fromthe paper supplier, which are not necessarily the same as the roll'scharacteristics on arrival at the corrugating site. For example, thespecific moisture content of the paper roll when it was shipped from thepaper supplier may have changed en route to the corrugator based on theatmospheric conditions during shipping and storage. A number ofconditions, such as those discussed above regarding hydro- andhygroexpansion, can impact the moisture content of the paper duringshipment and storage. For example, when humidity is elevated, the paperfibers are more likely to gain moisture based on equilibriumthermodynamics. Conversely, when humidity is low, the paper fibers aremore likely to lose moisture via the same mechanism. Such dataconcerning the transit conditions of the paper roll, or concerning otherfactors that may impact or have affected the hygroexpansivity of thepaper after the origin date, also may be collected and assessed.

Additionally, the corrugator may know or collect data regarding warp andwashboarding characteristics for corrugated products that have come offof the specific corrugator to be used.

All of the foregoing data (collectively the “Corrugator Input Data”) arecollected and input to the respective Corrugator Control Terminal 600for making a given corrugated composite. The Corrugator Control Terminal600 then aggregates and transmits the Corrugator Input Data via thenetwork 610 to the Central Site 620, where a processor evaluates thatdata and compares it to datapoints that have been aggregated in theCentral Site's 620 Data Storage, which have been cross-referenced tohygroexpansivity attribute values for paper layers. The Central Site 620can conduct a statistical analysis, described more fully below, toidentify a particular stored hygroexpansivity attribute value that islikely to be most representative of the papers (hereafter a “PredictiveHygroexpansivity Attribute Value”) whose data have been stored based oncomparing with all the cross-classified datapoints that are received inthe Corrugator Input Data for a given paper to be used. Based on thePredictive Hygroexpansivity Attribute Value, and knowing other datapoints from the Corrugator Input Data (such as data for an opposingliner, downstream, post-corrugation conditions, etc.), the Central Site620 determines “Moisture Conditioning Setpoints” for each such linerconcerning the amount of moisture and the amount of thermal energy toimpart to the liner pre-adhesion, most likely to achieve desired (andideally opposing-liner matched) post-corrugation hygroexpansive behaviorbased on the Corrugator Input Data.

The Central Site 620 then transmits these Moisture ConditioningSetpoints to the respective Corrugator Control Terminal 600, which thenuses them to operate the moisture-conditioning apparatus for therespective corrugator. Such moisture-conditioning apparatus is known,e.g. from the '802 patent, and can include a thin-film metering systemas well as drum heaters as discussed above, and again more fully below.

As the disclosed network-based system is used and collects more data fordifferent papers, and for the same papers used at different locationsand under different conditions, both its accuracy and precision inselecting appropriate Moisture Conditioning Setpoints based on a givenset of Corrugator Input Data will increase. But for a given corrugatorsite it also is contemplated that some measure of localized fine-tuningalso may be desired, e.g. to compensate for conditions that may impactpost-warp or corrugator-emergent warpage and which cannot be readilyquantified and fed to the Central Site 620 in the Corrugator Input Data.Accordingly, a robust system that utilizes the disclosed network-basedsystem for selecting Moisture Control Setpoints also may utilize somemeasure of localized feedback control to fine-tune those setpointsduring operation of the corrugator.

Various methods of warp detection, including via laser, have been usedby corrugators in feedback-control loops in attempts to reduce warp.Such methods include measuring the level of warp on the corrugatedproduct immediately after it is produced. Unfortunately, by themselvesthese methods have proven unreliable at best, and mostly ineffectivebecause much of the warp in corrugated products occurs some period oftime post-corrugation. So immediate post-corrugation laser-shapemeasurement has been an unreliable way to control post-warp. However,using the substantial excess-moisture application described above, andespecially when coupled with the network-based control system disclosedhere, a much higher degree of predictable, reliable dimensionalstability than before will be available for corrugated composites comingoff of the corrugator. Accordingly, measurements taken immediatelypost-corrugation will be more likely to approximate the long-term shapeand configuration of the corrugated product.

Using the disclosed system, post-warp measured at 24 hours, andpreferably at 48 hours, compared the conformation (i.e. flatness ordegree of curvature) of a corrugated composite board as or just after itemerges from the corrugator, may be reduced or adjusted to be not morethan 5% relative deflection (i.e. change in the radius of curvaturedefining the degree of warpage), preferably not more than 3% or 2% ofsuch relative deflection, and most preferably not more than 1% of suchrelative deflection. In essence, the degree of curvature (if any) of theboard on exiting the corrugator will remain substantially flatter (or iftuned-in, then substantially constant) during these periods of time, andfor extended periods. Accordingly, with the degree of observablepost-warp having been materially reduced, one can now use laser-based(or other) post-corrugation shape-detection systems to fine-tune theMoisture-Conditioning Parameters coming from the Central Site 620, inorder that the shape of the board coming off of the corrugator can befine-tuned to precise or locally required conformations.

For example, some downstream converting equipment may operate moreefficiently if there is a well-defined degree of warpage(convexity/curvature) to the corrugated boards as-supplied to theconverting equipment. Using the present system, it is contemplated thata laser-shape measurement system can be used to tune in precise amountsof relative moisture to be applied to the opposing liners of a givencorrugated composite before they are adhered, in order to achieve justthe right degree of mis-match so that the final post-corrugated productpossesses a tuned degree of convexity; i.e. a predefined radius ofcurvature of the post-corrugated board. And because the network-basedsystem reliably ensures post-corrugation dimensional stability, thedegree of convexity/curvature measured immediately post-corrugation willbe sustained for an extended period post-corrugation—so that the shapecoming off the corrugator will be that introduced later to theconverting equipment.

In addition to utilizing local feedback-control systems to fine-tune theMoisture-Conditioning Parameters sent from the Central Site 620, thefeedback-control data also can be sent to the Central Site 620 as anadditional data parameter that can be cross-classified against theHygroexpansivity Attribute Values and their correlated Moisture-ControlParameters stored in the Central Site's Data Storage. Suchfeedback-control data then becomes another cross-classified datapointthe next time the same corrugator site supplies the same CorrugatorInput Data to make the same composite from the same starting materials,so that the resulting Moisture-Conditioning Parameters can be morefinely tuned directly from the Central Site 620, thus minimizing theneed for localized feedback-control intervention. They also can be usedto statistically model and calculate different Moisture ControlParameters for different corrugator sites who have supplied comparabledata as part of their own initial Corrugator Input Data. This willimprove the statistical calculation of initial Moisture-ControlParameters for operating a different corrugator controlled by adifferent Corrugator Control Terminal 600.

As described above, it is possible to adjust the hygroexpansivity ofindividual paper liners to the lowest common hygroexpansivity betweenthem before they are laminated to opposing sides of a web of mediummaterial. This can be an iterative process; i.e. to determine whatprecisely is the maximum degree of reduction in hygroexpansivityattainable for each of the opposing layers, in order to tune each forit. Using the disclosed network-based system, which aggregateshygroexpansivity attribute data, this can be achieved. Indeed, thedegree of anticipated or maximum hygroexpansivity reduction based onparticular Moisture-Conditioning Parameters and other prevailingconditions can be modeled for each liner web and recorded by the CentralSite 620. Then the Central Site can fine-tune subsequentMoisture-Conditioning Parameters for the opposing liner webs to tunethem to their least common value for hygroexpansivity reduction, basedon the prevailing conditions. Once the final hygroexpansivities of theindividual paper liners in a given composite are adjusted to match, theywould gain or lose moisture at the same rate and degree in the finalcorrugated product. This results in corrugated products that maintaintheir dimensional stability throughout and after the corrugationprocess.

As part of the Corrugator Input Data, sensors at the corrugator's sitecan measure atmospheric data that is unique to the specific location,including temperature, relative humidity, and pressure. Forecastedatmospheric conditions may also be input to the Corrugator ControlTerminal 600 based on how long the final corrugated product will bestored at the corrugator's location, or based on other, known downstreamconditions. For example, if the final corrugated product will be storedat the corrugator's location for 4 days, the forecasted atmosphericconditions for the four days following production of the finalcorrugated product may be added to the data compiled in CorrugatorControl Terminal 600, and assembled into the Corrugator Input Data to betransmitted to the Central Site 620. As part of that data, thecorrugator also supplies the desired characteristics of the finalcorrugated product, such as the desired physical dimensions and thetarget moisture content of the liners and medium after corrugation,which can be input by the corrugation operator.

Once transmitted to the Central Site 620, a local processor at that sitecan analyze the data and either look up corresponding PredictiveHygroexpansivity Attribute Values (and their associatedMoisture-Conditioning Parameters), or if none are present it cancalculate (such as through statistical modeling) such values based onthe Corrugator Input Data. In the latter event, such calculated valueswould be stored as a new set of cross-classified PredictiveHygroexpansivity Values and correlated Moisture-Conditioning Parameters,available the next time similar data are queried based on similar papercharacteristics from previous runs and the prevailing atmosphericconditions.

Such a statistical analysis can be based on multivariate statisticalprocess control, which allows for the extraction of data based onmultivariable data sets. Multivariate statistical process controlmethods are used to identify desired variables in a process and pinpointunderlying patterns within the data. The Central Site 620 will thusinclude a data-based model based on prior processes for generatingcorrugated products and which have supplied feedback concerning theefficacy of post-warp control using specific Moisture-ConditioningParameters. The data provided by the Corrugator Control Terminal 600 isanalyzed in light of the data-based model of the Central Site 620. TheCentral Site 620 will then determine whether any new data points areabnormal compared to existing data. If an abnormality is found, theCentral Site 620 will identify any potential variables that could havecaused the abnormality and determine the root cause. Following such ananalysis of specific Corrugator Input Data provided by a CorrugatorControl Terminal 600, a processor at or of the Central Site 620 candetermine whether to discount the particular Corrugator Input Data infuture determinations of future Predictive Hygroexpansivity AttributeValues based on the fact that particular data may constitute an outliercontrary to the predominant thrust of the overall data set.

When Moisture-Control Setpoints are supplied from the Central Site 620to a Corrugator Control Terminal 600, the local operator can reviewthose setpoints and either accept them or and make real-time adjustmentsif deemed necessary. If such adjustments are made, they, too, can besupplied to the Central Site 620 as additional datapoints of theCorrugator Input Data for cross-classification against determined orcalculated Hygroexpansivity Attribute Values and their correlatedMoisture-Control Setpoints. Alternatively, and as part of an automatedprocess, the supplied Moisture-Control Setpoints can be automaticallyimplemented by the Corrugator Control Terminal 600 to moisture conditioneach liner (and optionally medium) prior to the corrugation process.

As shown in FIG. 3, multiple Corrugator Control Terminals 600 may beconnected to the network 610, and thus to the Central Site 620, inparallel. As each Corrugator Control Terminal 600 uploads data to theCentral Site 620, the accumulated data is compiled into the data-basedmodel stored in the Central Site's Data Storage. With each usage, thedata underlying that model grows and the recommended Moisture-ControlSetpoints provided by the Central Site 620 become more refined. Forexample, the Central Site 620 can compare data from prior corrugationprocesses, including origin data for each paper roll, the desiredphysical dimensions and target moisture content of the liners and mediumafter corrugation, and atmospheric conditions during corrugation andstorage. With continued expansion of the Central Site 620 database, asoptimized moisture settings for a specific paper are adjusted over timebased on atmospheric conditions and desired physical properties of thefinal corrugated product, the Central Site 620 refines the analysis sothat the recommended Moisture-Conditioning Parameters for each liner andmedium to provide the highest potential of dimensional stability.

The Central Site 620 also serves as a check on the localized inputs ateach Corrugator Control Terminal 600. For example, when an operatorinputs process parameters into his local Corrugator Control Terminal600, the Central Site 620 can compare the input parameters with ones itwould have suggested based on its dataset and model to determine if theinput parameters would be predicted to yield non-ideal results, orresults outside of a threshold of allowable variance from predictedidealized results. If such an abnormality exists based on the parametersinput by the corrugator operator, the Central Site 620 can alert theoperator. This permits the operator to adjust the corrugating processparameters based on a data-driven, predictive model even if reasonsexist that he will not want to simply accept the Moisture-ConditioningParameters suggested by the Central Site 620. In some embodiments, asupervisor can lock out the entry of operating parameters by an operatorthat would result in a deviation from the supplied Moisture-ConditioningParameters by a predefined threshold, or which would be predicted toyield additional post-warp exceeding a predefined threshold.

The recommended Moisture-Conditioning Parameters from the Central Site620 provide benefits compared to conventional methods of adjusting themoisture content for liners and mediums. First, the Central Site 620recommends such setpoints for each individual liner and medium based ondata available not only from the paper supplier, but from the specificcorrugator site and other (even competitive) corrugator sites, who donot necessarily know or have access to one another's data. This resultsin paper-specific moisture control that provides reproduciblepost-corrugation dimensional stability for virtually any corrugatedcomposite, based on a big-data set aggregated from a variety of sourcesat different stages in the manufacturing process (from paper-rollmanufacture, through transport, to corrugation, and even converting andstorage), previously unavailable to any individual corrugator. Overtime, it is contemplated that the Moisture-Conditioning Parameterscalculated or modeled based on individual Corrugator Input Data willbecome so refined that localized feedback control may become redundanteven for fine-tuning purposes. Not only does this greatly reduce thetime and cost for individual corrugators to research and developmechanisms to account and tune for the hygroexpansive behavior ofcorrugating liners, but it is able to supply to them setpoints based ondata to which they otherwise never could have had access, including fromcompetitors. Because the Central Site 620 never supplies information toan individual Corrugator Control Terminal 600 concerning the source ofany particular data or the associated Moisture-Control Parametersdelivered in a given instance, no Corrugator Control Terminal 600 everis aware of who else is doing what, or where particular data came from.In this manner, competitive corrugators are able to improve their ownoperations, mutually benefiting from one another's data but withouthaving access to or knowing about one another's operations.

It is recognized that in certain instances, a particular corrugator maydecline to allow its data to be aggregated and used to provide suchpredictive modeling to supply Moisture-Control Parameters to itscompetitors. In such an instance, the big-data based modeling availableto other Corrugator Control Terminals 600 can be isolated from thatspecific corrugator, so that both his data is not available to supplysetpoints for others, and reciprocally that the big data is not utilizedto supply setpoints for the specific corrugator. In such case, theCentral Site 620 still can receive and aggregate Corrugator Input Datafrom the non-participating corrugator, but such data will be isolatedand maintained in a separate data file specific to that corrugator, andany predictive or statistical modeling of Hygroexpansivity AttributeValues and corresponding Moisture-Control Parameters will be limitedexclusively to data supplied by that corrugator—or to other publiclyavailable information.

Once the Central Site 620 has supplied Moisture-Conditioning Parametersfor a given set of Corrugator Input Data, the corrugator can implementthose parameters and begin (or continue) to operate. Generally speaking,all such parameters will be utilized to increase the moisture content ofa paper liner to greater than 10 wt. %, followed by heating, prior toadhering that liner to an adjacent layer to produce a corrugatedcomposite. Such Moisture-Conditioning Parameters include, but are notnecessarily limited to: the coating weight of excess moisture (greaterthan 10%) to be applied to each paper (liner) layer by the thin-filmmetering apparatus described below, and the amount of thermal energy tobe imparted thereto prior to adhesion to adjacent layers (e.g. viaheating drums, hot plates, etc.).

The method and system described herein may employ computing systems forprocessing information and controlling aspects of a Corrugator ControlTerminal and a corrugating apparatus 1000. For example, for thecorrugator Controls Terminals, the network, and the Central Site shownin FIG. 3, each terminal receives data from a paper roll and an operatorrelating to a process for preparing a final corrugated product.Generally, the computing systems include one or more processors.

The processor(s) of a computing system may be implemented as acombination of hardware and software elements. The hardware elements mayinclude combinations of operatively coupled hardware components,including microprocessors, communication/networking interfaces, memory,signal filters, circuitry, etc. The processors may be configured toperform operations specified by the software elements, e.g.,computer-executable code stored on computer readable medium. Theprocessors may be implemented in any device, system, or subsystem toprovide functionality and operation according to the present disclosure.The processors may be implemented in any number of physicaldevices/machines. For example, computer system of the central site mayinclude one or more shared or dedicated general purpose computersystems/servers to communicate with the network and each corrugatorcontrol terminal. Optionally, parts of the processing of the exampleembodiments can be distributed over any combination of processors forbetter performance, reliability, cost, etc.

The physical devices/machines can be implemented by the preparation ofintegrated circuits or by interconnecting an appropriate network ofconventional component circuits, as is appreciated by those skilled inthe electrical art(s). The physical devices/machines, for example, mayinclude field programmable gate arrays (FPGAs), application-specificintegrated circuits (ASICs), digital signal processors (DSPs), etc. Thephysical devices/machines may reside on a wired or wireless network,e.g., LAN, WAN, Internet, cloud, near-field communications, etc., tocommunicate with each other and/or other systems, e.g., Internet/webresources.

Appropriate software can be readily prepared by programmers of ordinaryskill based on the teachings of the example embodiments, as isappreciated by those skilled in the software arts. Thus, the exampleembodiments are not limited to any specific combination of hardwarecircuitry and/or software. Stored on one computer readable medium or acombination of computer readable media, the computing systems mayinclude software for controlling the devices and subsystems of theexample embodiments, for driving the devices and subsystems of theexample embodiments, for enabling the devices and subsystems of theexample embodiments to interact with a human user (user interfaces,displays, controls), etc. Such software can include, but is not limitedto, device drivers, operating systems, development tools, applicationssoftware, etc. A computer readable medium further can include thecomputer program product(s) for performing all or a portion of theprocessing performed by the example embodiments. Computer programproducts employed by the example embodiments can include any suitableinterpretable or executable code mechanism, including but not limited tocomplete executable programs, interpretable programs, scripts, dynamiclink libraries (DLLs), applets, etc. The processors may include, or beotherwise combined with, computer-readable media. Example forms ofcomputer-readable media include a hard disk, any other suitable magneticmedium, CD-ROM, CDRW, DVD, any other suitable optical medium, RAM, PROM,EPROM, FLASH-EPROM, any other suitable memory chip or cartridge, acarrier wave, or any other suitable medium from which a computer canread.

The Central Site and Corrugator Control Terminals may also includedatabases for storing data. For example, the central site may includedifferent databases for storing individual data parameters from theCorrugator Input Data or for different categories of such data, such asatmospheric conditions, temperature and relative humidity, etc. One ormore additional database(s) may be used for storingphysical-characteristic information on each type of paper. Still furtherdatabases may be used to store cross-classified or correlated (orcalculated) Hygroexpansivity Attribute Values. The data entries in allsuch databases may be cross-classified or cross-referenced usingappropriate markers. Such databases may be stored on the computerreadable media described above and may organize the data according toany appropriate approach. For examples, the data may be stored inrelational databases, navigational databases, flat files, lookup tables,etc. Furthermore, the databases may be managed according to any type ofdatabase management software.

The invention has been described with reference to the exampleembodiments described above. Modifications and alterations will occur toothers upon a reading and understanding of this specification. Exampleembodiments incorporating one or more aspects of the invention areintended to include all such modifications and alterations insofar asthey come within the scope of the appended claims and their equivalents.

What is claimed is:
 1. A method of producing a corrugated product,comprising: a. adjusting a moisture content in a first face-sheet web toa first range of greater than 10 wt. % and up to 30 wt. % by applying afirst thin film of liquid to a first surface thereof; b. thereafterheating the first face-sheet web; c. thereafter bonding the firstsurface of the first face-sheet web to a first side of a fluted medium;d. adjusting a moisture content in a second face-sheet web to a secondrange of greater than 10 wt. % and up to 30 wt. % by applying a secondthin film of liquid to a first surface thereof; e. thereafter heatingthe second face-sheet web; and f. thereafter bonding the first surfaceof the second face-sheet web to a second side of said fluted medium,further comprising: measuring or assigning to said first face-sheet weba first hygroexpansivity attribute value, said moisture-contentadjustment therein being made based on said first hygroexpansivityattribute value; measuring or assigning to said second face-sheet web asecond hygroexpansivity attribute value, said moisture-contentadjustment therein being made based on said second hygroexpansivityattribute value; wherein the moisture adjustments in said first andsecond face-sheet webs followed by heating thereof yield respectivecooperating hygroexpansivities therein such that the corrugated productexhibits no more than 5% relative deflection in a radius of curvaturethereof at 24 hours after being made from said first and secondface-sheets and said fluted medium.
 2. The method of claim 1, furthercomprising: supplying to a central site corrugator input data relatedto: a) any or all of the specific first or second face-sheet webs or thecorrugated medium, b) characteristics of equipment used to make saidcorrugated product, c) prevailing atmospheric conditions, or d)anticipated downstream conditions of the corrugated product whenfinished; said central site assigning said first hygroexpansivityattribute value and said second hygroexpansivity attribute value basedon the corrugator input data; and said central site supplying a firstmoisture-conditioning setpoint for said first face-sheet web within saidfirst range based on said first hygroexpansivity attribute value, saidcentral site further supplying a second moisture-conditioning setpointfor said second face-sheet within said second range based on said secondhygroexpansivity attribute value, said first and secondmoisture-conditioning setpoints being adapted to yield said cooperatinghygroexpansivities.
 3. The method of claim 1, further comprising:supplying to a central site corrugator input data comprising datarelated to: a) any or all of the specific first or second face-sheetwebs or the corrugated medium, b) characteristics of equipment used tomake said corrugated product, c) prevailing atmospheric conditions, ord) anticipated downstream conditions of the corrugated product whenfinished; and receiving from the central site a firstmoisture-conditioning setpoint for said first face-sheet web and asecond moisture-conditioning setpoint for said second face-sheet web,which setpoints are based on the corrugator input data supplied to thecentral site, said moisture adjustments in said first and secondface-sheet webs being made according to the respective first and secondmoisture-conditioning setpoints.
 4. The method of claim 3, said firstand second moisture-conditioning setpoints being determined throughcomparison of the corrugator input data to comparable data available tothe central site, which comparable data have been previously correlatedto observed or calculated hygroexpansivity attribute values.
 5. Themethod of claim 3, wherein the moisture adjustments in said first andsecond face-sheet webs followed by heating thereof yield respectivecooperating hygroexpansivities therein such that the corrugated productexhibits no more than 1% relative deflection in the radius of curvaturethereof at 24 hours after being made from said first and secondface-sheets and said fluted medium.
 6. The method of claim 1, whereinthe moisture adjustments in said first and second face-sheet websfollowed by heating thereof yield respective cooperatinghygroexpansivities therein such that the corrugated product exhibits nomore than 1% relative deflection in the radius of curvature thereof at24 hours after being made from said first and second face-sheets andsaid fluted medium.
 7. A method of producing a corrugated product,comprising: a. adjusting a moisture content in a first face-sheet web toa first range of greater than 10 wt. % and up to 30 wt. % by applying afirst thin film of liquid to a first surface thereof; b. thereafterheating the first face-sheet web; and c. thereafter bonding the firstsurface of the first face-sheet web to a first side of a fluted medium,wherein the moisture adjustments in said first face-sheet web followedby heating thereof yields a first hygroexpansivity therein such that thecorrugated product exhibits no more than 5% relative deflection in aradius of curvature thereof at 24 hours after being made from said firstface-sheet and said fluted medium.
 8. The method of claim 7, wherein themoisture adjustments in said first face-sheet web followed by heatingthereof yields a first hygroexpansivity therein such that the corrugatedproduct exhibits no more than 1% relative deflection in the radius ofcurvature thereof at 24 hours after being made from said firstface-sheet and said fluted medium.